Distributed Oblivious RAM for Secure Two-Party Computation

  • Steve Lu
  • Rafail Ostrovsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7785)

Abstract

We present a new method for secure two-party Random Access Memory (RAM) program computation that does not require taking a program and first turning it into a circuit. The method achieves logarithmic overhead compared to an insecure program execution.

In the heart of our construction is a new Oblivious RAM construction where a client interacts with two non-communicating servers. Our two-server Oblivious RAM for n reads/writes requires O(n) memory for the servers, O(1) memory for the client, and O(logn) amortized read/write overhead for data access. The constants in the big-O notation are tiny, and we show that the storage and data access overhead of our solution concretely compares favorably to the state-of-the-art single-server schemes. Our protocol enjoys an important feature from a practical perspective as well. At the heart of almost all previous single-server Oblivious RAM solutions, a crucial but inefficient process known as oblivious sorting was required. In our two-server model, we describe a new technique to bypass oblivious sorting, and show how this can be carefully blended with existing techniques to attain a more practical Oblivious RAM protocol in comparison to all prior work.

As alluded above, our two-server Oblivious RAM protocol leads to a novel application in the realm of secure two-party RAM program computation. We observe that in the secure two-party computation, Alice and Bob can play the roles of two non-colluding servers. We show that our Oblivious RAM construction can be composed with an extended version of the Ostrovsky-Shoup compiler to obtain a new method for secure two-party program computation with lower overhead than all existing constructions.

Keywords

Oblivious RAM Cloud Computing Multi-Server Model Software Protection Secure Computation 

References

  1. 1.
    Ajtai, M.: Oblivious RAMs without cryptogrpahic assumptions. In: STOC, pp. 181–190 (2010)Google Scholar
  2. 2.
    Ajtai, M., Komlós, J., Szemerédi, E.: An O(n logn) sorting network. In: STOC, pp. 1–9 (1983)Google Scholar
  3. 3.
    Batcher, K.E.: Sorting networks and their applications. In: AFIPS Spring Joint Computing Conference, pp. 307–314 (1968)Google Scholar
  4. 4.
    Ben-Or, M., Goldwasser, S., Kilian, J., Wigderson, A.: Multi-prover interactive proofs: How to remove intractability assumptions. In: STOC, pp. 113–131 (1988)Google Scholar
  5. 5.
    Bloom, B.H.: Space/time trade-offs in hash coding with allowable errors. Commun. ACM 13(7), 422–426 (1970)CrossRefMATHGoogle Scholar
  6. 6.
    Boneh, D., Kushilevitz, E., Ostrovsky, R., Skeith III, W.E.: Public Key Encryption That Allows PIR Queries. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 50–67. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Boneh, D., Mazieres, D., Popa, R.A.: Remote oblivious storage: Making oblivious RAM practical. CSAIL Technical Report, MIT-CSAIL-TR-2011-018 (2011)Google Scholar
  8. 8.
    Chandran, N., Ostrovsky, R., Skeith III, W.E.: Public-Key Encryption with Efficient Amortized Updates. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 17–35. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Chor, B., Goldreich, O., Kushilevitz, E., Sudan, M.: Private information retrieval. In: FOCS, pp. 41–50 (1995)Google Scholar
  10. 10.
    Damgård, I., Meldgaard, S., Nielsen, J.B.: Perfectly Secure Oblivious RAM without Random Oracles. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 144–163. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Goldreich, O.: Towards a theory of software protection and simulation by oblivious RAMs. In: STOC, pp. 182–194 (1987)Google Scholar
  12. 12.
    Goldreich, O.: Foundations of Cryptography: Basic Tools. Cambridge University Press, Cambridge (2001)CrossRefMATHGoogle Scholar
  13. 13.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229 (1987)Google Scholar
  14. 14.
    Goldreich, O., Ostrovsky, R.: Software protection and simulation on oblivious RAMs. J. ACM 43(3), 431–473 (1996)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Goodrich, M.T.: Randomized shellsort: A simple oblivious sorting algorithm. In: SODA, pp. 1262–1277 (2010)Google Scholar
  16. 16.
    Goodrich, M.T., Mitzenmacher, M.: Privacy-Preserving Access of Outsourced Data via Oblivious RAM Simulation. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 576–587. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  17. 17.
    Goodrich, M.T., Mitzenmacher, M., Ohrimenko, O., Tamassia, R.: Oblivious RAM simulation with efficient worst-case access overhead. In: CCSW, pp. 95–100 (2011)Google Scholar
  18. 18.
    Goodrich, M.T., Mitzenmacher, M., Ohrimenko, O., Tamassia, R.: Privacy-preserving group data access via stateless oblivious RAM simulation. In: SODA, pp. 157–167 (2012)Google Scholar
  19. 19.
    Gordon, D., Katz, J., Kolesnikov, V., Malkin, T., Raykova, M., Vahlis, Y.: Secure computation with sublinear amortized work. Cryptology ePrint Archive, Report 2011/482 (2011)Google Scholar
  20. 20.
    Huang, Y., Evans, D., Katz, J., Malka, L.: Faster secure two-party computation using garbled circuits. In: USENIX Security Symposium (2011)Google Scholar
  21. 21.
    Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Cryptography with constant computational overhead. In: STOC, pp. 433–442 (2008)Google Scholar
  22. 22.
    Ishai, Y., Prabhakaran, M., Sahai, A.: Founding Cryptography on Oblivious Transfer – Efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  23. 23.
    Kirsch, A., Mitzenmacher, M., Wieder, U.: More Robust Hashing: Cuckoo Hashing with a Stash. In: Halperin, D., Mehlhorn, K. (eds.) ESA 2008. LNCS, vol. 5193, pp. 611–622. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  24. 24.
    Kreuter, B., Shelat, A., Shen, C.-H.: Towards billion-gate secure computation with malicious adversaries. Cryptology ePrint Archive, Report 2012/179 (2012)Google Scholar
  25. 25.
    Kushilevitz, E., Lu, S., Ostrovsky, R.: On the (in)security of hash-based oblivious RAM and a new balancing scheme. Cryptology ePrint Archive, Report 2011/327 (2011)Google Scholar
  26. 26.
    Kushilevitz, E., Lu, S., Ostrovsky, R.: On the (in)security of hash-based oblivious RAM and a new balancing scheme. In: SODA, pp. 143–156 (2012)Google Scholar
  27. 27.
    Lu, S., Ostrovsky, R.: Multi-server oblivious RAM. IACR Cryptology ePrint Archive, 2011:384 (2011)Google Scholar
  28. 28.
    Lu, S., Ostrovsky, R.: How to garble RAM programs. IACR Cryptology ePrint Archive, 2012:601 (2012)Google Scholar
  29. 29.
    Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: STOC, pp. 590–599 (2001)Google Scholar
  30. 30.
    Ostrovsky, R.: Apparatus system and method to efficiently search and modify information stored on remote servers, while hiding the access pattern. U.S. Patent Application No. 12,768,617 (April 27, 2010)Google Scholar
  31. 31.
    Ostrovsky, R.: Software Protection and Simulation On Oblivious RAMs. PhD thesis, Massachusetts Institute of Technology (1992)Google Scholar
  32. 32.
    Ostrovsky, R.: Efficient computation on oblivious RAMs. In: STOC, pp. 514–523 (1990)Google Scholar
  33. 33.
    Ostrovsky, R., Shoup, V.: Private information storage (extended abstract). In: STOC, pp. 294–303 (1997)Google Scholar
  34. 34.
    Osvik, D.A., Shamir, A., Tromer, E.: Cache Attacks and Countermeasures: The Case of AES. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 1–20. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  35. 35.
    Pagh, R., Rodler, F.F.: Cuckoo Hashing. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol. 2161, pp. 121–133. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  36. 36.
    Pinkas, B., Reinman, T.: Oblivious RAM Revisited. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 502–519. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  37. 37.
    Pippenger, N., Fischer, M.J.: Relations among complexity measures. J. ACM 26(2), 361–381 (1979)MathSciNetCrossRefMATHGoogle Scholar
  38. 38.
    Shi, E., Chan, T.-H.H., Stefanov, E., Li, M.: Oblivious RAM with O((logN)3) Worst-Case Cost. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 197–214. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  39. 39.
    Stefanov, E., Shi, E., Song, D.: Towards practical oblivious RAM. In: NDSS (2012)Google Scholar
  40. 40.
    Williams, P., Sion, R.: Usable PIR. In: NDSS (2008)Google Scholar
  41. 41.
    Williams, P., Sion, R., Carbunar, B.: Building castles out of mud: practical access pattern privacy and correctness on untrusted storage. In: ACM Conference on Computer and Communications Security, pp. 139–148 (2008)Google Scholar
  42. 42.
    Yao, A.C.-C.: Protocols for secure computations (extended abstract). In: FOCS, pp. 160–164 (1982)Google Scholar

Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Steve Lu
    • 1
  • Rafail Ostrovsky
    • 2
  1. 1.Stealth Software Technologies, Inc.USA
  2. 2.Department of Computer Science and Department of MathematicsUCLA Work done with consulting for Stealth Software Technologies, Inc.USA

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